Programs like filesystems typically have their own schedulers that aggregate writes, it would be an extreme performance hit if they wrote each checksum individu

Programs like filesystems typically have their own schedulers that aggregate writes, it would be an extreme performance hit if they wrote each checksum individually, as a separate I/O operation. They are certainly bundled with some other data that needs to be written. And if you are concerned about the compute rather than storage, then writing to a block device is still slow enough so that computing a checksum isn't important performance-wise.